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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

Quantum Field Theory 2

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Code Completion Credits Range
02KTPA2 Z,ZK 8 4P+2C
Lecturer:
Martin Štefaňák (guarantor), Petr Jizba
Tutor:
Václav Zatloukal
Supervisor:
Department of Physics
Synopsis:

Abstract:

The lecture aims at introducing the students to the Feynman’s functional integral and its applications. The focus is on broadening the knowledge of modern parts of relativistic and non-relativistic Quantum Field Theory and statistical physics. The content of the lecture can serve as a base for further study in fields of exactly solvable models, theory of critical phenomena, molecular chemistry and biochemistry or quantum gravity.

Requirements:
Syllabus of lectures:

Outline of the lecture:

1. First quantization with path integral

2. Second quantization and functional integral

2. Functional integrals, partition sum and Wick’s theorem

3. Noether’s theorem and anomalies

4. Perturbation expansion of Green’s functions with Feynman’s diagrams – scalar field, generating functionals W and Г

5. Grassmann’s variables and Berezin’s functional integral for fermionic fields

6. Perturbation expansion of Green’s functions with Feynman’s diagrams – fermionic fields

7. S-matrix and LSZ formalism

8. Goldstone’s theorem and Higgs mechanism

9. Calibration fields and their quantization

10. Callan-Symanzik equation of renormalization group and β function

11. Some spectral properties of 2-point correlation functions

Syllabus of tutorials:

Outline of the exercises:

Solving problems to illustrate the theory from the lecture.

Study Objective:
Study materials:

Key references:

[1] M. Blasone, P. Jizba and G. Vitiello, Quantum Field Theory and its Macroscopic Manifestations, Boson Condensation, Ordered Patterns and Topological Defects, (Imperial College Press, London, 2011)

[2] A. Altland and B. Simons, Condensed Matter Field Theory, (Cambridge University Press, Singapore, New York, 2013)

Recommended references:

[3] E. Fradkin, Field Theories of Condensed Matter Physics, (Cambridge University Press, New York, 2013)

[4] H. Kleinert, Particles and Quantum Fields, (World Scientific, London, 2017)

Note:
Time-table for winter semester 2020/2021:
Time-table is not available yet
Time-table for summer semester 2020/2021:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2021-01-27
For updated information see http://bilakniha.cvut.cz/en/predmet6237706.html